Find the critical values y, and xR for the given confidence level c and sample size n. c= 0.9, n=24 2 = (Round to three decimal places as needed.) (Round to three decimal places as needed.) %3D

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## Finding Critical Values for Chi-Square Distribution

**Problem Statement:**
Find the critical values \(\chi^2_L\) and \(\chi^2_R\) for the given confidence level \(c\) and sample size \(n\).

**Given:**
- Confidence level, \(c = 0.9\)
- Sample size, \(n = 24\)

**Instructions:**
1. Calculate \(\chi^2_L\).
2. Calculate \(\chi^2_R\).

*Note: Round to three decimal places as needed.*

### Chi-Square Critical Values:

\[ \chi^2_L = \quad \_\_\_ \quad \text{(Round to three decimal places as needed.)} \]

\[ \chi^2_R = \quad \_\_\_ \quad \text{(Round to three decimal places as needed.)} \]

Understanding the computation of these critical values allows for determining the threshold points in a chi-square distribution that correspond to the specified confidence level and degrees of freedom, which in this case is \(n - 1 = 23\). The critical values, one for the left tail (\(\chi^2_L\)) and one for the right tail (\(\chi^2_R\)), define the range where the true variance lies with 90% confidence.
Transcribed Image Text:## Finding Critical Values for Chi-Square Distribution **Problem Statement:** Find the critical values \(\chi^2_L\) and \(\chi^2_R\) for the given confidence level \(c\) and sample size \(n\). **Given:** - Confidence level, \(c = 0.9\) - Sample size, \(n = 24\) **Instructions:** 1. Calculate \(\chi^2_L\). 2. Calculate \(\chi^2_R\). *Note: Round to three decimal places as needed.* ### Chi-Square Critical Values: \[ \chi^2_L = \quad \_\_\_ \quad \text{(Round to three decimal places as needed.)} \] \[ \chi^2_R = \quad \_\_\_ \quad \text{(Round to three decimal places as needed.)} \] Understanding the computation of these critical values allows for determining the threshold points in a chi-square distribution that correspond to the specified confidence level and degrees of freedom, which in this case is \(n - 1 = 23\). The critical values, one for the left tail (\(\chi^2_L\)) and one for the right tail (\(\chi^2_R\)), define the range where the true variance lies with 90% confidence.
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